Is there a way to render an object invisible but still have it block view?
Use the holdout shader. Just be wary it will also not render anything else covered by the shaded object. It will not even render world texture.

EDIT: [

This is in cycles, BTW
You find this by going to the material tab, go to surface, click "use nodes". The default shader is Diffuse BSDF, but you can change it using this menu. Use mix shaders in the node editor if you want to mix it with something. "With a Holdout shader, you're basically saying, 'there's nothing here, not even background." When Cycles renders a material with a Holdout shader, it makes that section of rendered image completely transparent, with an alpha of zero. This can be useful in compositing, as the effect can give you a 3D mask" - Blender for Dummies I threw together a quick sample render with very high contrast colors, just to show what I mean. Be careful though, as you can see the mesh with the holdout shader does still cast a shadow.